English

Oil and water: a two-type internal aggregation model

Probability 2014-08-05 v1 Statistical Mechanics

Abstract

We introduce a two-type internal DLA model which is an example of a non-unary abelian network. Starting with n "oil" and n "water" particles at the origin, the particles diffuse in Z according to the following rule: whenever some site x has at least 1 oil and at least 1 water particle present, it "fires" by sending 1 oil particle and 1 water particle each to an independent random neighbor x+1 or x-1. Firing continues until every site has at most one type of particles. We establish the correct order for several statistics of this model and identify the scaling limit under assumption of existence.

Cite

@article{arxiv.1408.0776,
  title  = {Oil and water: a two-type internal aggregation model},
  author = {Elisabetta Candellero and Shirshendu Ganguly and Christopher Hoffman and Lionel Levine},
  journal= {arXiv preprint arXiv:1408.0776},
  year   = {2014}
}

Comments

47 pages, 3 figures

R2 v1 2026-06-22T05:20:09.554Z